**THE LAW OF VARIABLE PROPORTIONS**

The process of production, in turn, calls for a new exercise of economy, because the means of production are scarce in some cases and abundant in others. In the last analysis, all industry consists in moving materials from one place to another. That is all that the moving-picture machine, or the human eye as a mechanical device, would reveal. But the mind sees plans, purposes, and laws back of this process of moving materials. One of the great generalizations of the scientific observer is that all this moving of materials is for the purpose of getting things together in the right proportions. Of course there are purposes back of all this, but the observed fact is that every industrial purpose is carried out by getting materials together in the right proportion. All this moving of materials which the eye sees is dominated by the law of proportionality, and the skill of the producer consists first in knowing the right proportions in which to combine materials, and, second, in his ability to bring them together.

This applies everywhere from a chemical experiment to the irrigation of a desert, from the work of the artist in his studio to that of the farmer in his field. The chemist, however, works under a law of definite proportions, under which chemical elements have to be combined in exact mathematical ratios, whereas the greater part of the work of production is under the law of variable proportions. In the irrigation of a piece of land, for example, there are variable quantities of water which may be used in the growing of a crop. One cannot say that an exact quantity of water must be applied, otherwise there will be no crop at all, or that the slightest variation either way would utterly ruin the crop. Within fairly wide limits of moisture a crop can be grown, though within these limits the crop will vary somewhat—but not exactly—according to the quantity of moisture provided.

Wherever the law of variable proportions holds, that is, wherever the law of definite proportions does not hold, the product may vary whenever any of the factors which are necessary to its production varies; but the product will seldom vary in exact proportion as any single factor is varied. Adding one-tenth to the quantity of moisture in the soil will seldom, and only accidentally, result in the increase of exactly one-tenth to the crop. The same may be said with respect to fertilizer, or to any single element of fertility, with respect to the labor of cultivation, or with respect to any other single factor which enters into the determination of the size of a crop. Moreover, all this can be repeated with respect to any productive plant, say a factory, and of the factors of production which have to be combined in it.

The work of assembling the factors of production in any productive establishment, whether it be a shop, farm, factory, or transportation system, calls for a degree of knowledge and care comparable with that of the chemist in the assembling of chemical elements, though, as stated before, the chemist must follow definite formulæ with mathematical precision, because of the law of definite proportions.

This law of variable proportions is difficult to state concisely, but the following formulæ may serve to give a fairly accurate notion as to its meaning and import. Let us assume that three factors, x, y, and z, are necessary to get a certain desirable product, which we will call p.

If it should be found by experiment that the addition of one unit of x resulted in (1) more than 110 p, or (2) 110 p, that would indicate that the proportion of x to the other factors y and z was too low. Since an additional unit of x will result in such a large increase in the product, it is evident that more of x will be strongly desired, as compared with more of y and z, for if there is too little of x in the combination there must be too much of y and z. If, however, it were found that the addition of one unit of x resulted in (4) 100 p—that is, no increase at all—or (5) in less than 100 p—that is, less than was produced before—it is obvious that the proportion of x to the other factors is too high. Consequently, more of x will be little desired as compared with y and z, because if there is too much of x in the combination there must be too little of y and z. But if the increase in x results in an increase of five units of product proportional increase, in the product, then the factors are nearing the right proportions. Whether it is better to increase x by one unit will then depend upon the cost of x and the value of the increased product. Let us suppose that the increase in x results in an increase of five units of product (150 p). If one unit of x cost less than five units of p, it will be profitable to increase the factor x from 10 to 11; otherwise it will not.

Of course the formula and all that comes after it could be repeated with respect to y or z, as well as of x, if either were regarded as the variable factor. x, y, and z may represent labor, land, and capital in industry in general; they may represent different grades of labor in any industry; they may represent nitrogen, potash, and phosphorus in the soil; or they may represent any group of factors anywhere combined to get any product. The essential thing to remember is that in any combination the scarcest factor is the limiting factor, and the product will vary more directly with that than with any other. Since the variation in the product follows more sharply the variation in this scarce factor than that of any of the more abundant factors in the combination, it is not uncommon to speak of the scarcest factor as having the highest productivity. Whether that be an accurate use of terms or not, there is not the slightest doubt that it will be most highly prized, will command the highest price, and will need to be economized most carefully. This formula and the remarks under it will serve to bring out the underlying physical fact of productivity upon which the law of supply and demand is based.